def exercise_volume():
for (a,b,c) in ((1,2,3), (2,3,1), (3,1,2)):
for vertices in permutations(((1,1,1), (1+a,1,1), (1,1+b,1), (1,1,1+c))):
t = tetrahedron(vertices)
assert t.vertices == vertices
vol = a*b*c/6
assert approx_equal(t.volume(), vol)
# regular tetrahedron
for vertices in permutations(((1,1,1), (1,-1,-1), (-1,1,-1), (-1,-1,1))):
t = tetrahedron(vertices)
assert approx_equal(t.volume(), 8/3)
def exercise_volume():
for (a, b, c) in ((1, 2, 3), (2, 3, 1), (3, 1, 2)):
for vertices in permutations(
((1, 1, 1), (1 + a, 1, 1), (1, 1 + b, 1), (1, 1, 1 + c))):
t = tetrahedron(vertices)
assert t.vertices == vertices
vol = a * b * c / 6
assert approx_equal(t.volume(), vol)
# regular tetrahedron
for vertices in permutations(
((1, 1, 1), (1, -1, -1), (-1, 1, -1), (-1, -1, 1))):
t = tetrahedron(vertices)
assert approx_equal(t.volume(), 8 / 3)
def exercise_gradients(n_points):
eta = 1e-6
for i in xrange(n_points):
v = tuple((random(), random(), random()) for j in xrange(4))
t = tetrahedron(v)
g = t.gradients()
for j in xrange(4):
for k in xrange(3):
(tm, tp) = tuple(tetrahedron(
v[:j] + (v[j][:k] + (v[j][k] + h,) + v[j][k+1:],) + v[j+1:])
for h in (-eta, eta))
dv = (tp.volume() - tm.volume())/(2*eta)
assert approx_equal(dv, g[j][k]), (j,k)
def exercise_gradients(n_points):
eta = 1e-6
for i in range(n_points):
v = tuple((random(), random(), random()) for j in range(4))
t = tetrahedron(v)
g = t.gradients()
for j in range(4):
for k in range(3):
(tm, tp) = tuple(
tetrahedron(v[:j] + (v[j][:k] +
(v[j][k] + h, ) + v[j][k + 1:], ) +
v[j + 1:]) for h in (-eta, eta))
dv = (tp.volume() - tm.volume()) / (2 * eta)
assert approx_equal(dv, g[j][k]), (j, k)